The FunctionAverage(f(x), x=a..b) command returns the average value of the expression  on the interval from a to b. By using options, you can specify that the command returns a plot or inert integral instead.

If the independent variable can be uniquely determined from the expression, the parameter x need not be included in the calling sequence.

The average value of an expression f(x) from  to  is the value of the expression:

The opts argument can contain any of the Student plot options or any of the following equations that (excluding output) set plot options.

averageoptions = list

A list of options for the plot of the average value of . By default, the average is plotted as a solid blue line. For more information on plot options, see plot/options.

functionoptions = list

A list of options for the plot of the expression .  By default, the expression is plotted as a solid red line. For more information on plot options, see plot/options.

output = value, integral, or plot

This option controls the return value of the function.

* output = value specifies that the average value is returned. Other options are ignored if output = value.  This is the default.

* output = integral specifies that the expression  times the inert integral with the integrand f(x) is returned. Other options are ignored if output = integral.

* output = plot specifies that a plot, which shows the expression and its average value from a to b, is displayed.

showaverage = true or false

Whether the average of the expression  over the range  is plotted. By default, the value is true.

showfunction = true or false

Whether the expression  is plotted.  By default, the value is true.

caption = anything

A caption for the plot.

The default caption is constructed from the parameters and the command options. caption = "" disables the default caption. For more information about specifying a caption , see plot/typesetting.